Finite Group Databasebeta

C2×#13129728 #16779996

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#13129728

Splittings

SylowC13 ⋊ C2×#1301

Subgroups

subgroupG/H
centerC23(C2×#261)⋊C4
commutatorC2×C4×C13C2×C42
FrattiniC42C22×#261
FittingC2×C13×C4⋊C8C4
socleC23×C13#95
prime radicalC23×D13C4⋊C4
cosocleC42×D13C23
hypercenterC2×C4⋊C8#261
hypocenterC13C2×#1301
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1086645);